Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long i, n, h, A, B, tar = 0;
  scanf("%lld", &n);
  for (int i = 1; i < sqrt(double(2 * n)); i++) {
    A = (i * (i + 1)) / 2;
    ;
    long long l = i, r = sqrt(double(2 * n)), mid = (l + r) / 2;
    while (l <= r) {
      B = mid * (mid + 1) / 2;
      if (A + B == n) {
        tar = 1;
        goto aaa;
      } else if (A + B < n) {
        l = mid + 1;
        mid = (l + r) / 2;
      } else {
        r = mid - 1;
        mid = (l + r) / 2;
      }
    }
  }
aaa:
  if (tar == 0)
    cout << "NO" << endl;
  else
    cout << "YES" << endl;
}